What are the formulas governing blender's exponential easing for animation fcurves?
The math used can be found here, the calculations for the parameters used can be found here.

The calculation used for exponential ease in is -

change * powf(2, 10 * (time / duration - 1)) + begin


The curve is calculated between a start keyframe (begin) and an end keyframe, time is the time elapsed since the start key and duration is the total time between start and end, change is the amount the keyed value changes between keyframes.

The commit that adds this and the other nine interpolation types to blender contains links to easings.net and robertpenner.com/easing/ as the source of the calculations.